Partial derivatives of economic functions
Partial derivatives as instantaneous slopes
The first example reflects a utility function with two inputs, or goods, consumed. The syntax to find the partial derivatives is to type "Derivative(a(x,y), x)" - you tell Geogebra to take the derivative of the function a(x,y) with respect to x. You then do the same thing for y.
The second example is a total revenue example (advertising). Here, I omitted the reference to the arguments so that the syntax is simply "Derivative(d, x)" to calculate the derivative of the Total revenue function with respect to x. I then solved for the zero of the partial derivative of d with respect to y. Be careful of the syntax for that case. You need to tell Geogebra what you're solving for, f(x,y)=0, but then also pass Geogebra the list of inputs that you want it to solve for, which should be the same as the arguments of your function, {x,y}.